Nicholas J. Gaul

Modified Bayesian Kriging for Noisy Response Problems for Reliability Analysis

Abstract : This paper develops a new modified Bayesian Kriging (MBKG) surrogate modeling method for problems in which simulation analyses are inherently noisy and thus standard Kriging approaches fail to properly represent the responses. The purpose is to develop a method that can be used to carry out reliability analysis to predict probability of failure. The formulation of the MBKG surrogate modeling method is presented, and the full conditional distributions of the unknown MBKG parameters are presented. Using the full conditional distributions with a Gibbs sampling algorithm, Markov chain Monte Carlo is used to fit the MBKG surrogate model. A sequential sampling method that uses the posterior credible sets for inserting new design of experiment (DoE) sample points is proposed. The sequential sampling method is developed in such a way that the newly added DoE sample points will provide the maximum amount of information possible to the MBKG surrogate model, making it an efficient and effective way to reduce the number of DoE sample points needed. Therefore, the proposed method improves the posterior distribution of the probability of failure efficiently. To demonstrate the developed MBKG and sequential sampling methods, a 2-D mathematical example with added random noise is used. It is shown how, with the use of the sequential sample method, the posterior distribution of the probability of failure converges to capture the true probability of failure. A 3-D multibody dynamics (MBD) engineering block-car example illustrates an application of the new method to a simple engineering example for which standard Kriging methods fail.

Reliability Analysis of Wind Turbine Blades for Fatigue Life under Wind Load Uncertainty

This study presents a methodology that analyzes the fatigue reliability of a composite wind turbine blade considering wind load uncertainty. To facilitate the reliability analysis of wind turbine design, the turbulent random wind field has been simulated and characterized by two random variables, 10-minute mean wind speed and 10-minute turbulence intensity factor. The well-known Weibull distribution of 10-minute mean wind speed has been validated by statistically analyzing measured wind speed data. A log-logistic distribution is first proposed to represent the distribution of 10-minute turbulence intensity factor. By using both the mean wind speed and the turbulence intensity factor, the chaotic characteristic of a random wind field can be accurately rendered. The uncertainties of parameters determining the Weibull and log-logistic distribution are further studied such that the spatiotemporal wind uncertainty can be accurately represented. A hierarchical expanded wind uncertainty representation method is proposed for reliability analysis of wind turbine blades. A comprehensive procedure, including random wind simulation, aerodynamic analysis, composite structural analysis and fatigue damage calculation has been realized to predict the fatigue life of a simulated blade model. The reliability of a 5-MW reference wind turbine blade is evaluated to investigate the effect of the spatiotemporal wind uncertainty towards fatigue life.

Development of a Conservative Model Validation Approach for Reliable Analysis

Abstract : Simulation models are approximations of real-world physical systems. Therefore, simulation model validation is necessary for the simulation-based design process to provide reliable products. However, due to the cost of product testing, experimental data in the context of model validation is limited for a given design. When the experimental data is limited, a true output PDF cannot be correctly obtained. Therefore, reliable target output PDF needs to be used to update the simulation model. In this paper, a new model validation approach is proposed to obtain a conservative estimation of the target output PDF for validation of the simulation model in reliability analysis. The proposed method considers the uncertainty induced by insufficient experimental data in estimation of predicted output PDFs by using Bayesian analysis. Then, a target output PDF and a probability of failure are selected from these predicted output PDFs at a user-specified conservativeness level for validation. For validation, the calibration parameter and model bias are optimized to minimize a validation measure of the simulation output PDF and the conservative target output PDF subject to the conservative probability of failure. For the optimization, accurate sensitivity of the validation measure is obtained using the complex variable method (CVM) for sensitivity analysis. As the target output PDF satisfies the user-specified conservativeness level, the validated simulation model provides a conservative representation of the experimental data. A simply supported beam is used to carry out the convergence study and demonstrate that the proposed method establishes a conservatively reliable simulation model.